NCERT Solutions for Class 9 Maths Chapter 13

Important NCERT Questions

Surface Areas and Volumes

NCERT Books for Session 2022-2023

CBSE Board, UP Board and Other state Boards

EXERCISE 13.8

Page No:236

Questions No:8

(i) Inside surface area of the dome,

(ii) volume of the air inside the dome.

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Let the internal radius of dome = r m

Internal surface area of dome = 2πr²

cost of white washing at the rate of Rs 2 = 2πr² × Rs 2 = Rs 4πr²

⇒ Rs 4πr = Rs 498.96

⇒ 4 × 22/7 × r² = 498.96

⇒ r² = (498.96×7)/4×22) = 39.69

⇒ r = √39.69 = 6.3 m

Therefore, the internal surface of dome = 2πr²

= 2 × 22/7 × (6.3)2

= 2 × 22/7 × 6.3 × 6.3

= 2 × 22 × 0.9 × 6.3

= 249.98 m²

Hence, the inside surface area of the dome is 249.48 m².

(II) Volume of the air inside the dome = 2/3πr³

= 2/3 × 22/7 × (6.3)³

= 2/3 × 22/7 × 6.3 × 6.3 × 6.3

= 2 × 22 × 0.3 × 6.3 × 6.3

= 523.9 cm³

Hence, the volume of the air inside the dome is 523.9 cm³.